Factorise by grouping method:

$a^{2} x^{2} + (a x^{2} + 1) x + a$

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Solution

$a^{2} x^{2} + (a x^{2} + 1) x + a = a^{2} x^{2} + a + (a x^{2} + 1) x = a (a x^{2} + 1) + x (a x^{2} + 1) = (a x^{2} + 1) (a + x)$

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